Answer
$x=-5$
Work Step by Step
Isolate the square root on one side. Then square both sides and put all terms on one side. Factor by trial and error to solve for $x$. One of the answers does not work.
$\sqrt {2x+19}-8=x$
$\sqrt {2x+19}=x+8$
$(\sqrt {2x+19})^2=(x+8)^2$
$x^2+16x+64=2x+19$
$x^2+14x+45=0$
$(x+5)(x+9)=0$
$x=-9,-5$
$\sqrt {2\times-9+19}-8\ne-9$
$x=-5$
